Details

analyze1.1s (9.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

Compiler

Compiled 30 to 25 computations (16.7% saved)

sample47.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
9.0ms	141×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify142.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	37

prune8.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 9.7b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(/.f64 2 (*.f64 r r))
5.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
7.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.1b	(.f64 r (.f64 w w))

rewrite78.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
48×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`div-inv_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64`

Counts

4 → 166

Calls

4 calls:

23.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
15.0ms	(.f64 r (.f64 w w))
13.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
4.0ms	(/.f64 2 (*.f64 r r))

series562.0ms (4.8%)

Counts

4 → 32

Calls

4 calls:

261.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
193.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
80.0ms	(.f64 r (.f64 w w))
28.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 1608 to 1379 computations (14.2% saved)

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4948	3966
1	4948	3966

prune372.0ms (3.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	185	13	198
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	187	13	200

Merged error: 2.5b

Counts

200 → 13

Compiler

Compiled 6476 to 3810 computations (41.2% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
1.1b	(/.f64 2 (*.f64 r r))
5.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
7.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite74.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`add-cube-cbrt_binary64`
35×	`associate-r_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`difference-of-squares_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 179

Calls

4 calls:

22.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
10.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.0ms	(/.f64 2 (*.f64 r r))

series692.0ms (5.9%)

Counts

4 → 38

Calls

4 calls:

258.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
213.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
192.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
28.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 1875 to 1599 computations (14.7% saved)

simplify94.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4974	4562
1	4974	4562

prune394.0ms (3.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	207	10	217
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	218	12	230

Merged error: 0.0b

Counts

230 → 12

Compiler

Compiled 7043 to 4103 computations (41.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 r)
1.1b	(/.f64 2 (*.f64 r r))
1.5b	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite155.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

378×	`times-frac_binary64`
247×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
241×	`add-exp-log_binary64`
225×	`cbrt-prod_binary64`
184×	`add-cube-cbrt_binary64`
151×	`add-cbrt-cube_binary64`
107×	`cbrt-unprod_binary64` `prod-exp_binary64`
92×	`cbrt-undiv_binary64` `div-exp_binary64`
42×	`difference-of-squares_binary64`
32×	`associate-/r*_binary64`
21×	`distribute-lft-out--_binary64`
9×	`pow1_binary64` `associate-/l*_binary64` `div-inv_binary64` `frac-times_binary64`
6×	`associate-*r/_binary64`
5×	`associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`associate-r_binary64` `pow1/3_binary64` `associate-/r/_binary64` `*-commutative_binary64`

Counts

4 → 363

Calls

4 calls:

49.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
15.0ms	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.0ms	(/.f64 2 (*.f64 r r))
1.0ms	(cbrt.f64 r)

series917.0ms (7.9%)

Counts

4 → 28

Calls

4 calls:

447.0ms	(/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))
330.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (/.f64 (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))) (.f64 r w))) (/.f64 (cbrt.f64 r) (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
108.0ms	(cbrt.f64 r)
32.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 2089 to 1669 computations (20.1% saved)

simplify165.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

391 → 391

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	11856
1	4961	11856

prune1.4s (12%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	391	0	391
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	391	12	403

Merged error: 0.0b

Counts

403 → 12

Compiler

Compiled 19446 to 11554 computations (40.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
1.1b	(/.f64 2 (*.f64 r r))
3.8b	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.1b	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))

rewrite57.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`pow1_binary64` `add-sqr-sqrt_binary64`
30×	`cbrt-unprod_binary64` `prod-exp_binary64`
27×	`*-un-lft-identity_binary64`
26×	`associate-l_binary64`
22×	`times-frac_binary64`
19×	`pow-prod-down_binary64`
18×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-*l/_binary64`
6×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64`
1×	`associate-/r*_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 127

Calls

4 calls:

17.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
14.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
6.0ms	(.f64 (.f64 r w) w)
5.0ms	(/.f64 2 (*.f64 r r))

series456.0ms (3.9%)

Counts

4 → 28

Calls

4 calls:

263.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
99.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
65.0ms	(.f64 (.f64 r w) w)
30.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 1336 to 1126 computations (15.7% saved)

simplify61.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5726	2726

prune215.0ms (1.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	155	12	167

Merged error: 0.0b

Counts

167 → 12

Compiler

Compiled 4545 to 2673 computations (41.2% saved)

regimes1.3s (10.8%)

Compiler: Compiled 19077 to 14619 computations (23.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	55
1	130	55

end0.0ms (0%)

sample3.2s (27.6%)

Algorithm

1×

intervals

Results

530.0ms	8000×	body	128	valid
321.0ms	4765×	body	128	invalid

Compiler

Compiled 2963 to 2274 computations (23.3% saved)

Details

analyze1.1s (9.2%)

sample47.0ms (0.4%)

simplify142.0ms (1.2%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

rewrite78.0ms (0.7%)

series562.0ms (4.8%)

simplify122.0ms (1%)

prune372.0ms (3.2%)

localize17.0ms (0.1%)

rewrite74.0ms (0.6%)

series692.0ms (5.9%)

simplify94.0ms (0.8%)

prune394.0ms (3.4%)

localize24.0ms (0.2%)

rewrite155.0ms (1.3%)

series917.0ms (7.9%)

simplify165.0ms (1.4%)

prune1.4s (12%)

localize18.0ms (0.2%)

rewrite57.0ms (0.5%)

series456.0ms (3.9%)

simplify61.0ms (0.5%)

prune215.0ms (1.8%)

regimes1.3s (10.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (27.6%)

Profiling